A little bit late for this question, but if you:
cat /path/to/repo/.git/config
You will see the url of the repository which will include the reponame:
[core]
repositoryformatversion = 0
filemode = true
bare = false
logallrefupdates = true
ignorecase = true
precomposeunicode = true
[remote "origin"]
url = https://github.com/your_git_user_name/your_git_repo_name.git
fetch = +refs/heads/*:refs/remotes/origin/*
[branch "master"]
remote = origin
merge = refs/heads/master